I tested with the seed
If i play against yakalir, the player 1 (second player) always timeout. Always. If i'm the second player, i timeout. If yakalir is second player, he timeout.
Then i tested against reCurse. If i'm player 0 i never timeout. If i'm player 1 i always timeout. reCurse never timeout, no matter the positions.
If i modify my code to prevent it to take all the second for the first turn, i never timeout.
I have no timeout in the arena. It's IDE specific. And it's specific to the second player position.
Conclusion: I don't know what you are doing in the IDE for the second player, but it's evil and the timeout calculation is wrong.